Sensing Beyond Barriers: Theory, Algorithms and Applications

通过成像和传感获取数据已经成为我们存在的一个常见方面，并有助于扩展人类的视觉和感知。无论是用于细胞计数的显微镜，还是旨在透过雾看东西的最新版本的自动驾驶汽车；这种传感装置价格昂贵，功能有限。例如，自动驾驶汽车的摄像头在驶出隧道时，可能会因为暴露在过多的光线下而变白。在许多应用程序中，硬件（捕获数据）和算法（从数据中恢复有意义的信息）被视为解耦的实体；首先捕获数据，然后提取信息。因此，基于硬件的限制，可以从数据中恢复的内容是有限的。我们能超越这些限制吗？本研究的目的是通过协同设计实现硬件和算法之间的协同平衡，从而打破数据捕获和成像中普遍存在的限制，从而使不可见变为可见。我们试图回答的问题包括：我们能否用低成本的传感器（如微软Kinect）进行生物成像？我们能捕获超出通常动态范围的信息吗？我们可以通过推断细胞的几何形状来无创地对血细胞进行分类吗？我们能消除照片中的反射吗？我们能透过扩散介质看到东西吗？这些问题要求我们超越传统的障碍（例如，动态范围，时空分辨率，捕获数据的速度等）。本提案中的工作依赖于一种协同设计方法，其中精心优化的捕获过程产生计算编码的测量结果，其中使用恢复算法对信息进行解码。这种方法被用来修改硬件和开发新的算法来恢复信息。应用领域从生物成像（细胞分类、荧光寿命成像、太赫兹光谱）、消费者成像（自动驾驶汽车）到新型传感硬件的概念化。考虑了三个特定的障碍：(1)动态范围障碍。我们建议使用由模操作非线性映射的记录测量。这是一种全新的感知或数字化信息的方式，在很大程度上尚未被探索。我们的初步工作表明，与香农的采样理论相关联的奈奎斯特率的简单修正允许从模信息中恢复带宽有限的信号。值得注意的是，采样界与阈值无关。在本论文中，我们研究了更大的信号类别，包括正弦和信号、稀疏信号和平滑信号，以及它们与到达方向估计和波束形成等应用领域的联系。(2)决议障碍。从低通滤波测量中恢复尖峰是一个经典问题，被称为超分辨率。然而，在许多实际情况下，由于传播和传输的物理特性，脉冲或滤波器可能会失真。现有的信号模型不能很好地处理这种情况。受光谱学、探地雷达、光声成像和超宽带阵列等问题的启发，我们的实验建立在这些问题的基础上，在这项工作中，我们朝着从时变脉冲中恢复峰值的方向迈出了一步，并准备了非理想超分辨率的算法。此外，当脉冲或滤波器平滑且不一定带宽受限时，稀疏反褶积的最佳带宽选择是本工作中要解决的一个开放问题。(3)带宽屏障。我们在特殊仿射傅里叶变换的背景下定义了带宽的概念，它推广了一些众所周知的变换。这使我们能够准备一个统一的方法来研究采样理论，它适用于更广泛的信号模型。我们的算法在跨学科和多大学合作的帮助下通过实验获得的数据进行验证

Data capture via imaging and sensing has become a common aspect of our existence and helps extend human vision and perception. Whether it is a microscope used for cell counting or the latest version of autonomous vehicle which aims to see through the fog; the sensing apparatus is expensive and limited in functionality. For example, the cameras of a self-driving car may white out due to exposure to excessive light when coming out of a tunnel.In many of applications, hardware (that captures data) and algorithms (which recover meaningful information from data) are treated decoupled entities; first capture data, extract information later. Hence, there is a limit to what can be recovered from the data based on the limitations of the hardware. Can we go beyond such limitations?The purpose of this research is to achieve a synergistic balance between hardware and algorithms by means of a co-design, so that popularly held limits in data capture and imaging can be broken, thus making the invisible, visible.Questions that we seek to answer include: Can we do bio-imaging with low-cost sensors (e.g. Microsoft Kinect)? Can we capture information beyond the usual dynamic range? Can we non-invasively classify blood cells by inferring cell geometry? Can we remove reflections in photographs? Can we see through diffusive media? These questions require us to go beyond the conventional barriers (e.g. dynamic range, spatio-temporal resolution, how fast the data is captured etc).The work in this proposal relies a co-design approach where carefully optimized capture process yields computationally encoded measurements from which the information is decoded using recovery algorithms. This approach is used to modify hardware and develop new algorithms to recover information. Application areas span from bio-imaging (cell-classification, fluorescence lifetime imaging, terahertz spectroscopy), consumer imaging (autonomous vehicles) to conceptualization of new sensing hardware. Three specific barriers are considered: (1) Dynamic Range Barrier. We propose the use of recording measurements that are non-linearly mapped by modulo operations. This is a fundamentally new way of sensing or digitising information and is largely unexplored. Our initial work shows that a simple correction to the Nyquist rate linked with Shannon's sampling theory allows for recovery of a bandlimited signal from modulo information. Remarkably, the sampling bound is independent of the the threshold. In this proposal we study a larger class of signals including sum-of-sinusoids, sparse signals and smooth signal and their link with application areas such as direction-of-arrival estimation and beamforming.(2) Resolution Barrier. Recovering spikes from low-pass filtered measurements is a classical problem and is known as super-resolution. However, in many practical cases of interest, the pulse or filter may be distorted due to physical properties of propagation and transmission. Such cases can not be handled well by existing signal models. Inspired by problems in spectroscopy, ground penetrating radar, photoacoustic imaging and ultra-wide band arrays, on which we base our experiments, in this work we take a step towards recovering spikes from time-varying pulses and prepare algorithms for non-ideal super-resolution. Furthermore, when the pulse or filter is smooth and not necessarily bandlimited, optimial bandwith selction for sparse-deconvolution is an open problem that is addressed in this work. (3) Bandwidth Barrier. We define the notion of bandwidth in context of Special Affine Fourier transforms which generalises a number of well known transformations. This allows us to prepare a unifying approach for studying sampling theory which is applicable to a wider class of signal models. Our algorithms are validated on experimentally acquired data with the help of inter-disciplinary and multi-university collaborations